We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fast-scale chaos and slow-scale periodicity can emerge subsequently to a sequence of Hopf bifurcations. The resulting time trace thereby consists in chaotic oscillations "breathing" periodically at a significantly lower frequency. Experimental evidence of this type of dynamics in delayed dynamical sys...

Time-delayed systems are found to display remarkable temporal patterns the dynamics of which split into regular and chaotic components repeating at the interval of a delay. This novel long-term behavior for delay dynamics results from strongly asymmetric nonlinear delayed feedback driving a highly damped harmonic oscillator dynamics. In the corresponding virtual space-time representation, the b...

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability cr...

A formal framework for the analysis of Hopf bifurcations in delay differential equations with a single time delay is presented. Closed-form linear algebraic equations are determined and the criticality of bifurcations is calculated by normal forms.

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations ẏ(t) =Ay(t) +A1y(t−∆) +F(t, y(t), yt) + (Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate cont...

Synchronization in a bidirectionally coupled system with a finite time-delay in coupling is studied using Josephson junction as a model system. Using the LyapunovKrasovskii method a sufficient condition for the stability of synchronization is obtained and it is found to be independent of the time-delay. The sum of the Lyapunov exponents transverse to the synchronization manifold is evaluated. N...

In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through a...

A way for treating general delayed systems with uncertain delays in both the numerator and denominator is shown. The proposed procedure is demonstrated by an example. A simple controller is derived via algebraic theory and the structured singular value, which treats uncertain time delay in both the numerator and denominator of an anisochronic system. The overall performance is verified by simul...

Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated with a delayed process but instead use an estimated average delay time. In an effort to examine the validity of this approach, we study systems with significa...

Dead-time or delay is a common problem in the processing industry. Sensors, actuators and transport phenomena often contribute to delay the process response or to prevent immediate action. Current control technology offers various alternatives to analyze and control delay systems. Among the most widely applied techniques are internal model control (IMC) and, to a lesser extent, model predictive...